I was dropping the front dif today and completely forgot to disconnect vent hose (big dummy move by me). Looks the the hose broke.

I am new to these cars and am not sure how the hose connects to the differential. Do I need to order a special part? All I see is a hose and the little hole on the dif, if there was another part I can't find it.

 

What year is your Ranger?

Looks like a Dana 35 SLA differential, so 1998 and up Ranger 4x4

In this picture you can see what should be in that hole: https://www.therangerstation.com/tec..._sla_cad-1.PNG

I think these were threaded in so external piece broke off and threaded part may still be in there and needs to be unscrewed??

Never had to replace one so not sure were to get one, most auto parts stores sell replacement axle vents, just not sure on the size for your model
These are also called axle breathers

Its not a "valve", its just an open vent/hole so as the oil in differential heats up and cools down the air pressure inside is equalized to outside air pressure, so no oil is forced out of seals and gaskets
The hose is often used on 4x4s so water can't get in to differentials, front or rear, in higher water crossings, or MUD, lol, end of these hoses should have a filter or loose cap so bugs don't build nests in them